| Through a simulation study with different design conditions (sample sizes at two levels ranging from 5 to 50, intraclass correlation ranging from 0.05 to 0.40), this study intends to provide some general guidelines about adequate sample sizes at two levels under different intraclass correlations (ICC) conditions for a viable two level HLM analysis (e.g., reasonably unbiased and accurate parameter estimates, reasonable power for detecting between-group variance). Because educational data typically have ICCs ranging from 0.1 to 0.2, we focus our discussions about adequate sample sizes under ICC - 0.15 as a representative condition. We discuss ranges of sample sizes that are inadequate or adequate for statistical power, relative bias, and accuracy of individual parameter estimates. To better choose adequate sample sizes under ICC = 0.1 and 0.2, we also examine effects of ICCs smaller or larger than 0.15 on sample size requirements. Unlike previous studies that dogmatize "minimum" sample size requirement for various purposes, the current study, with more detailed simulation designs for small sample sizes and ICCs, provides numerous options of "adequate" sample sizes under various ICC conditions. By providing these options and well-documented simulation results, this study emphasizes that "adequate" sample sizes at either level 1 or level 2 can be adjusted according to different interests in parameter estimates, different expectation of statistical power, and different ranges of tolerable bias and accuracy. Under different ICC conditions, we help readers identify level-1 sample size, level-2 sample size or both as the source of variation in relative bias or accuracy for a certain parameter estimate. This will assist researchers in making better decisions for selecting adequate sample sizes in HLM analysis. A limitation of this study is that we did not examine strength and weakness of different estimation algorithms (e.g., ML, REML, and FML) to produce unbiased or accurate parameter estimates. |
